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March, 1994 Local Asymptotic Minimax Risk Bounds for Asymmetric Loss Functions
Yoshiji Takagi
Ann. Statist. 22(1): 39-48 (March, 1994). DOI: 10.1214/aos/1176325356

Abstract

Hajek established a local asymptotic minimax risk bound for appropriate symmetric loss functions and also gave a necessary condition for the risk of an estimator to attain the lower bound. We extend these results to the case of asymmetric loss functions. The asymmetry brings about the shift of location of the loss functions. Besides, the optimal estimator that attains the bound is shown to have asymptotic normal distribution with asymptotic bias.

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Yoshiji Takagi. "Local Asymptotic Minimax Risk Bounds for Asymmetric Loss Functions." Ann. Statist. 22 (1) 39 - 48, March, 1994. https://doi.org/10.1214/aos/1176325356

Information

Published: March, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0804.62032
MathSciNet: MR1272074
Digital Object Identifier: 10.1214/aos/1176325356

Subjects:
Primary: 62F12
Secondary: 62C20, 62E20

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 1 • March, 1994
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